DRAFT VERSION AUGUST 6, 2019 Preprint typeset using LATEX style emulateapj v. 12/16/11 COOLING+HEATING FLOWS IN GALAXY CLUSTERS: TURBULENT HEATING, SPECTRAL MODELLING, AND COOLING EFFICIENCY ; ; ; ; MOHAMMAD H. ZHOOLIDEH HAGHIGHI1 2 3,NIAYESH AFSHORDI2 3 4, AND HABIB. G. KHOSROSHAHI1 1School of Astronomy, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran 2Perimeter Institute for Theoretical Physics, 31 Carolines St. North, Waterloo, ON, N2L 2Y5, Canada 3Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran 4Department of Physics and Astronomy, University of Waterloo, 200 University Ave. West, Waterloo, ON, N2L 3G1, Canada Draft version August 6, 2019 ABSTRACT The discrepancy between expected and observed cooling rates of X-ray emitting gas has led to the cooling flow problem at the cores of clusters of galaxies. A variety of models have been proposed to model the observed X-ray spectra and resolve the cooling flow problem, which involves heating the cold gas through different mechanisms. As a result, realistic models of X-ray spectra of galaxy clusters need to involve both heating and cooling mechanisms. In this paper, we argue that the heating time-scale is set by the magnetohydrodynamic (MHD) turbulent viscous heating for the Intracluster plasma, parametrised by the Shakura-Sunyaev viscosity parameter, α. Using a cooling+heating flow model, we show that a value of α ' 0:05 (with 10% scatter) provides improved fits to the X-ray spectra of cooling flow, while at the same time, predicting reasonable +0:63 cooling efficiency, cool = 0:33-0:15. Our inferred values for α based on X-ray spectra are also in line with direct measurements of turbulent pressure in simulations and observations of galaxy clusters. This simple picture unifies astrophysical accretion, as a balance of MHD turbulent heating and cooling, across more than 16 orders of magnitudes in scale, from neutron stars to galaxy clusters. Keywords: intracluster medium galaxies: clusters: individual (Hydra A, A2029, A2199, A496, A85) galaxies: cooling flow problem: active galactic nucleus (AGN): 1. INTRODUCTION inadequate and additional heating or cooling mechanisms The Intracluster Medium (ICM) of galaxy clusters consists should be incorporated into the model. Moreover, X-ray spec- of a plasma that is almost entirely ionized. This hot plasma ra- troscopy shows that the temperature drop toward the center is diates mostly in X-ray band which leads to a significant cool- limited to about a factor of three. The cooling seems to be ing of the ICM. At constant pressure, the cooling time of a frozen precisely in the region where we expect more rapid plasma is the gas enthalpy divided by the energy lost per unit cooling. In general, it appears that there is no strong evidence volume per unit time: for any significant amount of cold X-ray emitting gas (below 1/3 of the maximum temperature) in any cluster (Peterson & 5nkBT Fabian 2006). tcool ≡ ; (1) 2nenH Λ(T;Z) There exist different manifestations of the cooling-flow problem: According to Peterson et al.(2003), there is the soft where Λ(T;Z) is the cooling function in terms of temperature X-ray cooling-flow problem and the mass sink cooling-flow T and metallicity Z, n is the particle number density, and kB is problem. The soft X-ray cooling-flow problem refers to the the Boltzmann’s constant. In the cores of clusters, the cooling discrepancy seen between the predicted and observed soft X- time dips below 5 × 108 yr, i.e. the inferred radiative cool- ray spectrum, e.g. the lack of expected emission lines from a ing time of the gas in the central part, where X-ray emission gas cooling to low temperatures at the core of the cluster. The is sharply peaked, is much shorter than the age of the clus- mass sink cooling-flow problem refers to the lack of colos- ter, which suggests the existence of cooling flow. The stan- sal mass deposition in cooling clusters from the hypothesized arXiv:1806.08822v2 [astro-ph.GA] 4 Aug 2019 dard cooling flow model can be derived by combining con- cooling-flow plasma. tinuity, Navier-Stokes and energy conservation equation that, Many mechanisms have been proposed to prevent the gas after simplification, leads to: from cooling to low temperatures at the centers of cooling flows, such as the electron thermal conduction (Zakamska & dL 5k 1dp X = M_ B - : (2) Narayan 2003) , Mechanical heating of infalling gas in dense dT 2µmp ρdT core systems (Khosroshahi et al. 2004) and turbulent heat- In the case of constant pressure, we get the standard isobaric ing (Zhuravleva et al. 2014), though the lead suspect amongst cooling flow model: them is mechanical heating by Active Galactic Nuclei (AGN). AGN outbursts produce winds and intense radiation that can dL 5Mk_ heat the gas. Produced weak shocks delay cooling of gas by X = B : (3) dT 2µm reducing gas density and increasing the total energy (David K p 2001; McNamara et al. 2005; Forman et al. 2005) or by com- X-ray spectroscopy has demonstrated that this model is pensating lost entropy of the gas (Fabian et al. 2005). More- over, viscous damping of sound waves generated by repeated * [email protected] AGN outbursts may represent a significant source of heating 2 (Fabian et al. 2003). Direct evidence for these sound waves !$ came from the spectra observed by the Hitomi X-ray satel- !" lite, which measured the plasma’s line-of-sight velocity dis- !% !" persion of 164 ± 10 km/s within the core of Perseus cluster. !# This supports the hypothesis that turbulent dissipation of ki- !" netic energy can supply enough heat to offset gas from cooling !$ !' ! ! (Hitomi Collaboration et al. 2016). $ !$ # In this paper,we provide a simple yet accurate thermody- !$ !# namic model for cooling+heating (or CpH) flows, which cap- ! tures the balance between turbulent heating and cooling in " !& cluster cores (e.g., Zhuravleva et al. 2014). We then show !# ! that the model can simultaneously explain the X-ray spectra $ and the observed turbulent energy of the cluster cores, using a single parameter α ' 0:1, for the Shakura-Sunyaev viscosity parameter, while at the same time, predict reasonable cool- Figure 1. Schematic illustration of cooling flow in each annulus. Here, we ing efficiency. As such, this picture also unifies astrophysical model temperature distribution within each annulus as a result of in-situ cool- accretion across 16 orders of magnitude in scale, from kilo- ing and heating processes. metres (around neutron stars and stellar black holes) to kilo- parsecs (in cores of galaxy clusters). injection into the system by viscous heating. To estimate the heating time, we note that waves (and weak shocks) produced 2. DATA AND SPECTRAL EXTRACTION by AGcluster ofNs can travel at most by speed of sound. As For this study, we use a sample of galaxy clusters presented a result, sound crossing time is the shortest time scale in the by Hogan et al.(2017). The sample consists of 5 galaxy clus- ICM. We further assume that heating or viscous time should ters observed with Chandra X-ray Observatory over long ex- be a multiple of sound crossing time posure times. All five clusters have a central cooling time R r 3µm ≤ 1×109 yrs (Cavagnolo et al. 2009) suitable for our intended t α-3=2t R p ; heat = sound = 3=2 = 3 (4) analysis. The data are obtained from the Chandra imaging α cs 5α kBT online repository and analyzed using CIAO version 4.7. Bad where R is the distance to the center of the cluster, and α < 1. pixels are masked out using the bad pixel map provided by the The α parameter quantifies the ratio of turbulent/magnetic to pipeline. Background flares are removed, and point sources thermal energy, and is very similar to the Shakura-Sunyaev are identified with the CIAO task WAVDETECT and masked viscosity parameter in accretion disks (Shakura & Sunyaev out in all subsequent analysis. Finally, the blank-sky back- 1973), as in a turbulent medium equipartition implies: grounds are extracted for each target, and the images are pre- 2 2 2 pared in the energy range 0.5–7.0 keV. In addition, cavities hv i ∼ hvAi ∼ αcs ; (5) and filaments within ICM were masked clear, since these re- gions are usually out of equilibrium. where v and vA are turbulent and Alfven speeds. The heating time is then given by the ratio of thermal energy nkBT by Because the cooling instabilities usually occur at small 2 1=2 2 hv i (.10 kpc) radii, we desire finely binned spectra in the cen- turbulent heating rate ρhv i R : tral cluster regions. Our example clusters have deep Chandra 2 data; as a result, choosing of annuli for spectral extraction is nkBT Rc R t ∼ ∼ s ∼ α-3=2t : heat 2 3=2 2 3=2 3=2 = sound (6) limited by resolution rather than the number of counts. ρhv i =R hv i α cs For each example cluster, concentric circular annuli are centered at the cluster center. The width of the central an- The viscosity parameter typically takes a value of α ∼ 0:01 - nulus is 3 pixels, where each pixel is 0.492 arcsec across. The 0:1 in magnetohydrodynamic (MHD) simulations of weakly width of each annulus increases in turn by 1-pixel until the magnetized plasmas (e.g., Salvesen et al. 2016). sixth annulus, beyond which the width of each annulus is 1.5 Now, the central idea of our proposal is that the main driver times the width of the previous one with a total number of of thermal distribution in ICM is a balance of cooling and 10 annuli per source.